m Atmospherical Refraction, 339 
In the two annexed tables ai^e given the mean of the ob- 
served zenith distances of the several stars ; and in the next 
column the mean refraction, computed from the formula which 
I proposed in my former paper; viz. tang* s; — 3.3^25 rx 
38", 1192 : and which has been applied to these observations, 
corrected for the barometer and thermometer. In the follow- 
ing column, the error or difference is shewn, between the 
computed and real zenith distances ; the assumed mean 
refraction, corrected by these errors, will give the mean re- 
fraction, which should have been applied. From these last 
quantities are deduced the respective values of (y) the co- 
efficient of r, and of x : and from the mean of the sixteen stars, 
the resulting numbers will bey = 3 ^342936, 
Having therefore reduced the whole sixteen by these mean 
values of y and x ; the error or difference is noted, when com- 
pared with the corrected mean refraction which should arise 
from observation. On a review of these errors, and noticing 
the mean state of the thermometer for each star, the errors 
seem to indicate a small correction. I assumed in my former 
paper, that the refraction as affected by the thermometer, 
varied in an arithmetical ratio of ,0021 for each degree of 
Fahrenheit's scale ; and the mean state to be at 45° for the 
thermometer without. Continuing the same mean state, and 
changing the ratio to ,0020, these errors will be affected. 
-Tohoo refraction, for each degree above and below 43®; 
which being applied, will reduce the final error, as shewn in 
the last column. 
In the same manner I proceeded to find the values of y and x, 
from the six lower stars, contained in the second table ; but 
the respective values of both y and x were variable, and each 
